Melt butter in a large skillet with a tight fitting lid over medium heat. When melted, add onions and cook, stirring often, until tender, about 5 minutes. Add orzo, and cook for an additional 2 to 3 minutes.
Add vegetable broth, raisins, nutmeg, mushrooms, and milk, and bring to a simmer. Add rice and sesame seeds. Stir, bring to a simmer, cover, and let steam for 20 minutes.